Browsing by Subject "approximation"

Now showing 1 - 15 of 15

Access status: Restricted ,
Aproksymacja funkcjonałów liniowych w modelach obliczeń kwantowym i randomizowanym
(Data obrony: 2017-06-14) Warzecha, Elżbieta
Wydział Matematyki Stosowanej
Access status: Restricted ,
Aproksymacja gęstości przejścia dla wielowymiarowego procesu dyfuzji
(Data obrony: 2013-05-20) Michalik, Janusz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Metody tworzenia i modyfikacji funkcji sklejanych na potrzeby opisu kształtu obiektów obserwowanych punktowo
(Wydawnictwa AGH, 2006) Lenda, Grzegorz
This paper has been dedicated to describe a spline function course modification methods. Only use of them lets the splines to become a useful and precise tool, which serves to approximate shapes of any engineering objects. Some of these methods should be always applied (parametrical description connected with a proper parameterization, appropriate selection of the boundary conditions), the others are advantageous in depending on the surface's shape, number and accuracy of measured points (additional points insertion, approximant splines), and the rest (NURBS splines) are worth to utilize only in an exceptional cases, when the great deformations are generated by spline functions. The connection of these methods with schedule of the appropriately regularity location of measured points, will lets to obtain good effects of the spline functions approximation.
Access status: Open Access ,
Możliwości poprawy dokładności aproksymacji krzywych składu materiałów uziarnionych
(Wydawnictwa AGH, 2010) Foszcz, Dariusz; Saramak, Daniel; Tumidajski, Tadeusz; Niedoba, Tomasz; Gawenda, Tomasz
The approximation adequacy of particle size distribution curves for various grained materials is very significant in many industrial processing investigations. The authors propose in the paper various approaches to this issue, indicating advantages and disadvantages of classical and non-classical statistical analyzes. On the basis of selected results of particle size distributions of certain grained material, the classical forms of approximated formulas were presented, i.e. GSA, Weibull and log-norm distribution functions. It was indicated that the acceptance of proper maximum particle size is difficult to determine and leads to application of the so-called censored distribution functions. Furthermore, the non-parametrical methods of approximation were applied, such as orthogonal Fourier series and kernel methods. Their application results usually in better adequacy of approximation, but they cannot be the basis for technological interpretation. Furthermore, the approximation by the least squared method was performed with application of weights. The best approximation results were obtained for the logistic distribution function.
Access status: Open Access ,
New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry
(Wydawnictwa AGH, 2021) Alpay, Daniel; Jørgensen, Palle E.T.
We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.
Access status: Open Access ,
Ocena zawartości popiołu w pokładach węgla za pomocą nieparametrycznych metod statystycznych
(2007) Niedoba, Tomasz
The paper presents the distribution of ash contents in coal, treated as the mixture of distributions taken from the individual coal beds. In purpose of their approximation, apart from traditional log-norm distribution function, the non-parametric statistical methods were applied: kernel method and orthogonal Fourier series method. The best results of approximation were then mixed and the risk probability of evaluating the ash contents in the whole deposit was estimated.
Access status: Open Access ,
On some application of biorthogonal spline systems to integral equations
(2005) Wronicz, Zygmunt
We consider an operator $P_N: L_p(I) \to S_n(\Delta_N)$, such that $P_Nf=f$ for $f\in S_n(\Delta_N)$, where $S_n(\Delta_N)$ is the space of splines of degree $n$ with respect to a given partition $\Delta_N$ of the interval $I$. This operator is defined by means of a system of step functions biorthogonal to $B$-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the approximation of the solution of this equation are given.
Access status: Open Access ,
Simple eigenvectors of unbounded operators of the type »normal plus compact«
(2015) Gil', Michael
The paper deals with operators of the form $A=S+B$, where $B$ is a compact operator in a Hilbert space $H$ and $S$ is an unbounded normal one in $H$, having a compact resolvent. We consider approximations of the eigenvectors of $A$, corresponding to simple eigenvalues by the eigenvectors of the operators $A_{n}=S+B_{n}$ ($n=1,2, \ldots$), where $B_n$ is an $n$-dimensional operator. In addition, we obtain the error estimate of the approximation.
Access status: Open Access ,
Solutions to p(x)-Laplace type equations via nonvariational techniques
(Wydawnictwa AGH, 2018) Avci, Mustafa
In this article, we consider a class of nonlinear Dirichlet problems driven by a Leray-Lions type operator with variable exponent. The main result establishes an existence property by means of nonvariational arguments, that is, nonlinear monotone operator theory and approximation method. Under some natural conditions, we show that a weak limit of approximate solutions is a solution of the given quasilinear elliptic partial differential equation involving variable exponent.
Access status: Open Access ,
Spectrum localization of a perturbed operator in a strip and applications
(Wydawnictwa AGH, 2021) Gil', Michael
Let $A$ and $\tilde{A}$ be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of $A$ lie in some strip. In what strip the spectrum of $\tilde{A}$ lies if $A$ and $\tilde{A}$ are »close«? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.
Access status: Open Access ,
Testy jakości dopasowania funkcji sklejanych do kształtów obiektów rzeczywistych
(Wydawnictwa AGH, 2005) Lenda, Grzegorz
This article was devoted to the tests which allow to rate practical usability of spline functions in wide rage shape describing process. There were proposed effective criterions, which allow to rate quality of splines arc to approximated object convergence. Those tests were performed for especially created simple models, which can be easily compared with any measured shape. By then it become possible to sum up the deformations arised from the spline functions describing techniques. The investigations results are especially useful for measuring points schedule planning, that way to let the curve or surface consists of them to be precisely fitted to the real measured object shapes.
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Twierdzenie Weierstrassa o aproksymacji wielomianami funkcji ciągłych na przedziale zwartym
(Data obrony: 2010-07-07) Pawińska, Karolina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wykorzystanie funkcji sklejanych do opisu powłokowych budowli inżynierskich
(Data obrony: 2015-02-27) Dynowska, Justyna; Basiak, Katarzyna
Wydział Geodezji Górniczej i Inżynierii Środowiska
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Wykorzystanie funkcji sklejanych do opisu powłokowych budowli inżynierskich
(Data obrony: 2015-02-27) Basiak, Katarzyna; Dynowska, Justyna
Wydział Geodezji Górniczej i Inżynierii Środowiska
Access status: Restricted ,
Złożoność i podatność zadania aproksymacji całek funkcji o nieskończonej liczbie zmiennych
(Data obrony: 2020-07-10) Majchrowski, Dawid
Wydział Matematyki Stosowanej